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The nature of manifolds of periodic points for higher dimensional integrable maps

Satoru Saito·Noriko Saitoh
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Abstract

By studying periodic points for rational maps on $\bm{C}^d$ with $p$ invariants, we show that they form an invariant variety of dimension $p$ if the periodicity conditions are `fully correlated', and a set of isolated points if the conditions are `uncorrelated'. We present many examples of the invariant varieties in the case of integrable maps. Moreover we prove that an invariant variety and a set of isolated points do not exist in one map simultaneously.

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Satoru Saito, Noriko Saitoh. 2005-12-22. The nature of manifolds of periodic points for higher dimensional integrable maps. https://arxiv.org/abs/math-ph/0508063

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